![]() 1 a) Use the chain rule to find the derivative df(. Letting \(g(x) = 2x\) and \(f(x) = \sin(x)\), we observe that \(C(x) = f(g(x))\). This homework is due Wednesday, 10/12 (Monday 10/10 is Columbus day and no class), rsp. 217.\), we see that if \(C(x) = \sin(2x)\), then \(C'(x) = 2 \cos(2x)\). Calculus AB/BC 3.1 The Chain Rule - YouTube 0:00 / 15:20 Introduction Calculus: Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions Calculus AB/BC 3. Hardy, ``A course of Pure Mathematics,'' Cambridge University Press, 1960, 10th Edition, p. For instance, (2.5.14) d d x ( ln ( anything)) 1 anything ( anything) ( anything) anything. Because of this, one can become familiar with the basic process and learn patterns that facilitate finding derivatives quickly. One approach is to use the fact the "differentiability" is equivalent to "approximate linearity", in the sense that if $f$ is defined in some neighborhood of $a$, thenį'(a) = \lim_&\rightarrow 0 = F'(y)\,f'(x) One of the cool applications of the chain rule is that we can compute derivatives of inverse functions: Example: Find the derivative of the natural logarithm function log(x). The Chain Rule is used often in taking derivatives. With one additional rule, we will have the power to take the derivative of any.
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